Arectangular prism has the following dimensions. length: 18 inches width: 1 foot height: 14 inches if all the dimensions of this prism are tripled, what will be the surface area of the new figure? 3,816 in.2 7,632 in.2 27,216 in.2 11,448 in.2

11,448 in²

Step-by-step explanation:

The area can be computed from ...

... A = 2(LW +H(L+W))

For the given prism, the area will be ...

... A = 2(18·12 +14(18+12)) = 2(216 +420) = 1272 . . . . in²

The area of a similar figure with dimensions 3 times as long will be 3² times as much. The area of the new figure is ...

... A = 3²×(1272 in²) = 11,448 in²

11,448 in.2

Step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.